Uniquely Hamiltonian characterizations of distance-hereditary and parity graphs.
McKee, Terry A. (2008)
The Electronic Journal of Combinatorics [electronic only]
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McKee, Terry A. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Igor Fabrici, Erhard Hexel, Stanislav Jendrol’ (2013)
Discussiones Mathematicae Graph Theory
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A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.
Hopkins, Brian (2004)
International Journal of Mathematics and Mathematical Sciences
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Erhard Hexel (2017)
Discussiones Mathematicae Graph Theory
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The H-force number h(G) of a hamiltonian graph G is the smallest cardinality of a set A ⊆ V (G) such that each cycle containing all vertices of A is hamiltonian. In this paper a lower and an upper bound of h(G) is given. Such graphs, for which h(G) assumes the lower bound are characterized by a cycle extendability property. The H-force number of hamiltonian graphs which are exactly 2-connected can be calculated by a decomposition formula.
Jan Kratochvíl, Dainis A. Zeps (1987)
Acta Universitatis Carolinae. Mathematica et Physica
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Z. Skupień (1989)
Banach Center Publications
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Fleischner, H., Horák, P., Širáň, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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